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# Article

 Title: Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$ (English) Author: Skalák, Zdeněk Language: English Journal: Applications of Mathematics ISSN: 0862-7940 (print) ISSN: 1572-9109 (online) Volume: 48 Issue: 2 Year: 2003 Pages: 153-159 Summary lang: English . Category: math . Summary: We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution ${\mathbf u}$ belongs to $L^\infty (0,T,L^3(\Omega )^3)$, then the set of all possible singular points of ${\mathbf u}$ in $\Omega$ is at most finite at every time $t_0\in (0,T)$. (English) Keyword: Navier-Stokes equations Keyword: partial regularity MSC: 35B65 MSC: 35D10 MSC: 35Q10 MSC: 35Q30 MSC: 76D03 MSC: 76D05 idZBL: Zbl 1099.35089 idMR: MR1966346 DOI: 10.1023/A:1026046211510 . Date available: 2009-09-22T18:13:05Z Last updated: 2020-07-02 Stable URL: http://hdl.handle.net/10338.dmlcz/134524 . Reference: [1] L. Caffarelli, R. Kohn and L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations.Comm. Pure Appl. Math. 35 (1982), 771–831. MR 0673830, 10.1002/cpa.3160350604 Reference: [2] H. Kozono: Uniqueness and regularity of weak solutions to the Navier-Stokes equations.Lecture Notes Numer. Appl. Anal. 16 (1998), 161–208. Zbl 0941.35065, MR 1616331 Reference: [3] H. Kozono, H. Sohr: Remark on uniqueness of weak solutions to the Navier-Stokes equations.Analysis 16 (1996), 255–271. MR 1403221, 10.1524/anly.1996.16.3.255 Reference: [4] J. Neustupa: Partial regularity of weak solutions to the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$.J. Math. Fluid Mech. 1 (1999), 309–325. MR 1738173, 10.1007/s000210050013 Reference: [5] Y. Taniuchi: On generalized energy inequality of the Navier-Stokes equations.Manuscripta Math. 94 (1997), 365–384. MR 1485443, 10.1007/BF02677860 Reference: [6] R. Temam: Navier-Stokes Equations.North-Holland, Amsterdam-New York-Oxford, 1977. Zbl 0383.35057, MR 0769654 .

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